This invention relates to seismic-data processing, and particularly to an improved method for migrating seismic data having steeply-dipping reflector horizons.
In reflection seismic profiling, seismic signals are generated at or near the surface of the earth. Normally these seismic signals are considered to be in the form of a compressional wave field. As the signals propagate downward into the earth they are reflected and diffracted by discontinuities in the subsurface. Some of the signals are returned upward to the surface of the earth where they are detected by suitable seismic sensors. The returned signals are usually in the form of a train of seismic waves that are received over a predetermined time interval such as 10 seconds (s).
Along the surface of the earth above a zone of interest, many sensors may be deployed along a line or grid. Each sensor is usually in the form of an electro-mechanical transducer which converts the detected seismic signals into corresponding electrical signals. The electrical signals generated by each sensor correspond in amplitude and phase as a function of frequency to that of the received seismic wave train. The electrical signals from each sensor are transmitted over conductors to a remote recording unit for later processing.
The recorded seismic signals do not provide a true cross-section of the subsurface. They represent only the two-way travel time of the signals generated at the surface to a reflector and back to the surface. The reflected signals reaching the surface propagate in the form of ever-expanding wave fronts. In a non-uniform medium, variations in the velocity of propagation tend to influence and modify the direction of propagation and are accompanied by mutual interference of wave fronts. In zones of sudden changes along geologic interfaces such as faults, a portion of the seismic signal undergoes diffraction. Consequently the record of the detected signals represents a distorted image of the subsurface; an image which has undergone a complicated process of focusing, de-focusing, interference and diffraction. A numerical process for correcting these propagation effects in the data is the process of migration.
By far, the majority of migrations done today still fall into the category of time migration. In routine processing of large three dimensional (3-D) seismic surveys, computational efficiency and migration accuracy, always at issue, become primary concerns. High-accuracy migration techniques, whose speed limitations were tolerable for smaller surveys, may be unacceptably slow for large 3-D seismic surveys. Thus, for 3-D imaging and other reasons there continues to be interest in improving time-migration algorithms.
Many algorithms have been proposed for time migration, each with strengths and weaknesses. Most migration methods work well when dips are moderate and velocities are well behaved. However, those that perform well for steep dips and extreme velocity gradients tend to be less efficient. Now that steep-dip-information is routinely preserved by dip-moveout (DMO) processing for both 2-D and 3-D data, migration algorithms must be able to properly image steep dips. In addition to imaging steep dips accurately, the ideal time-migration algorithm would also correctly handle vertical velocity variations, honor the associated ray bending, and be computed efficiently. Also, it must accommodate some degree of lateral velocity variation.
In all but one of these ideal traits, Stolt's frequency-wavenumber (f-k) migration would be the method of choice. It is extremely fast relative to other migration techniques and has unlimited dip accuracy. Although it is strictly valid only in the constant-velocity setting, with Stolt's stretching of data to pseudo-depth and associated modification to the wave equation, it can also handle mild velocity variations both vertically and laterally. The only disadvantage to Stolt's f-k migration technique is that, for significant vertical velocity variation and steep dips, migration errors become unacceptable.